Mechanical oscillators are an essential component of practically every electronic system requiring a frequency reference for time keeping or synchronization and are also widely used in frequency-shift based sensors of mass, force, and magnetic field. Currently, micro- and nano-mechanical (collectively referred to as “micromechanical” herein) oscillators are being developed as an alternative to conventional oscillators, e.g. quartz oscillators, supported by their intrinsic compatibility with standard semiconductor processing and by their unprecedented sensitivity and time response as miniaturized sensing devices.
Generally, synchronization is possible when the frequency of an externally applied harmonic perturbation, Ωs, lies close enough to the oscillator's frequency Ω0, such that |Ωs−Ω0|<ΔΩ where 2ΔΩ is the synchronization range. Usually, the larger the interaction with the external harmonic perturbation, the further the frequency can be shifted and the larger the synchronization range. Additionally, the width of the synchronization range decreases as the amplitude of the linear oscillator increases. In other words, the ability to change the frequency of operation to an external harmonic perturbation decreases as the self-sustained drive force of the linear oscillator is increased.
Unfortunately, as the dimensions of the vibrating structures are reduced to the micro- and nano-scale their dynamic response at the amplitudes needed for operation frequently becomes nonlinear, with large displacement instabilities and excessive frequency noise considerably degrading their performance. These factors would seem to preclude micromechanical oscillator systems, specifically the micro- and nano-resonators, from being used in timing applications.